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The Hindu tradition is composed of a number of darsanas, or philosophical systems (Padhi and Padhi 221). This should not surprise the keen observer of Hinduism as the religion itself encapsulates a variety of theological, ritual, and philosophical schools of thought and practice. Among the latter is found the Mimamsa darsana, the philosophical school of Vedic interpretation and apologetics. The Mimamsa philosophical system is also important for underscoring the ritualistic nature of the early Vedic literature and for its rigorous epistemological contributions to Hindu philosophy to bolster the truth contained in the Vedas.

The earliest exposition of the Mimamsa darsana is that of the Hindu writer Jaimini. His Mimamsa-Sutra contains over 2,500 aphorisms and is estimated to have been written in 200 CE (Padhi and Padhi 222). Scholars do not credit Jaimini with the creation of the Mimamsa system, but do recognize his systematic presentation of the oral traditions and interpretations of Mimamsa as foundational to the philosophical school of thought (Dasgupta 370). Jaimini’s Mimamsa-Sutra is divided into 12 chapters, 60 sections, and covers nearly 1000 topics. In this significant work Jaimini espouses the general rules (nyayas) with which to distinguish dharma, that is, action in accord with the cosmic order, from adharma, action that is not in proper accord with the cosmos (Padhi and Padhi 222). As such, the Mimamsa-Sutra elucidates the number of sacrifices and rituals that existed in the Hindu tradition at that time. Perhaps the greatest contribution of Jaimini’s work, and of the Mimamsa darsana more generally, is its epistemological contribution to the understanding of knowledge as to how it can be interpreted and derived from the Vedas, the holy scriptures of the Hindu tradition (Padhi and Padhi 222).

The oldest extant commentary on Jaimini’s Mimamsa-Sutra is the Sabarabhasya (Bronkhorst 1). This work was followed by other expositions contained in the Slokavartika in the eighth century and the Prakaranapancika in the ninth century (Clooney 51). A more succinct expression of Mimamsa’s philosophical position was put forward in the Manameyodaya, which was begun by Narayanabhattatiri around 1590 and finished by Narayanasudhi a century later (Clooney 51). The system of Mimamsa articulated by Jaimini and developed by the aforementioned commentaries is also known as Purva-Mimamsa. The name reflects Jaimini’s interpretation (mimamsa) of the earlier Vedic texts, more specifically, the ritually oriented Brahmanas (Padhi and Padhi 219). This distinguishes Purva-Mimamsa from the hegemonic Hindu philosophy of Vedanta, which is also known as Uttara-Mimamsa for its interpretive focus of the chronologically later Vedic texts, namely the Upanisads (Clooney 53). Although scholarship suggests that there exists a great deal of continuity between Purva and Uttara-Mimamsa [For further discussion on the continuity between Mimamsa and Vedanta see Bronkhorst (2007)], the two systems are often studied separately (Clooney 53). Consequently, Vedanta philosophy shall receive cursory treatment in the present discussion.

As previously stated, the primary aim of Jaimini’s Mimamsa-Sutra is to address those actions that are conducive to the realization of dharma (Arnold np). In doing so, the Mimamsa darsana shifts the ideological focus away from the principal Hindu concern of liberation (moksa) from the cycle of rebirth, and toward an orthopraxis, or correct performance, of the brahminic rituals of the Vedic texts. With the attainment of heaven (syarga) and success in the life hereafter hanging in the balance, it becomes essential for the Mimamsa philosopher to establish the orthodoxy of the Vedic ritualistic injunctions (Bronkhorst 1). Jaimini maintains that the characteristics (laksana) of dharma can only be known by means of Vedic injunctions (codana) and testimony (sabda) (Arnold np). As a result, the secondary focus of the Mimamsa darsana is to function as an apologetic school in defense of the Vedic scriptures. As such, the primary concern of subsequent Mimamsa theorists is to demonstrate the intrinsic validity (svatah pramanya) of the religious truth contained within the Vedas (Arnold np). Consequently, the Mimamsa system is heavy laden with discussions pertaining to semantics and grammar (Hiriyanna 299). In their simplest form, the Mimamsakas attempt to uncover the very principles according to which the Vedas were written so as to reveal the truths contained within them (Hiriyanna 298).

Arnold astutely observes that the philosophical project of the Mimamsakas to prove the intrinsic validity of Vedic language using the Vedas themselves seems counterintuitive from the perspective of Western philosophy. Francis Clooney, however, argues that this is not surprising given the epistemological position of Mimamsa. Clooney clarifies that Mimamsa regards truth as right knowledge (prama), which may be known by way of pramanas (hereafter, means of right knowing) (Clooney 45). Jaimini himself conceded three pramanas: perception, inference, and verbal testimony. However, he contended that the word (sabda) of the Vedas alone is the only infallible means of knowledge (Padhi and Padhi 225-245). As such, Mimamsa theorists maintain that the ritual words of the Vedas are firmly intertwined with the ritual realities they endorse (Clooney 52). This is derived from Jaimini’s proposition that one should appeal to as few unseen realities as possible, a notion not all that unlike Occam’s Razor in Western philosophy. Consequently, religious truth is best understood in terms of what is observable, that is, the language and ritual directives of the Vedas. From this it naturally follows that the orthopraxis of said rituals serve as positive affirmation of truth in and among the community of believers (Clooney 51-52).

Although continuity exists between Mimamsa and the other Hindu darsanas, it does depart rather significantly from the Vaiseshika, Nyaya, Samkhya, and Yoga schools of philosophical thought (Padhi and Padhi 221). Mimamsa is set apart primarily by its emphasis on the sole authority of the Vedic scriptures as the epistemological source of eternal truth. In order to preserve the eternal status of the Vedas, Mimamsa largely does away with the Hindu doctrines of creation and dissolution as well as rejects the notion of deities external to the Vedas, resulting in a deification of the holy scriptures themselves (Padhi and Padhi 249). Francis Clooney recognizes that appeals to gods would move the authority of the Vedas to a source external to and higher than the scriptures. As such, Mimamsa apologists refute the existence of any such deities so as not to displace the sole authority of Vedic scriptures (Clooney 51).

The Mimamsa darsana is but one of many attempts to articulate truth and the nature of the cosmos in the Hindu tradition. Its epistemological insight grants the scholar a privileged view of truth as it relates to the sacred Vedic literature revered by Hindus. Understanding Mimamsa’s emphasis and exposition of orthopraxy is essential to understanding the complex nature of brahminic rituals in Hinduism. Although Vedanta in all its continuity has taken over the mainstream of Hindu philosophical thought, a comprehensive understanding of Mimamsa is essential to understand the complex interaction of truth and ritual in the Hindu tradition, as it has been both understood and practiced throughout history and as such practices evolve today.

Clooney, Francis X. (2001) “From Truth to Religious Truth in Hindu Philosophical Theology.” In Religious Truth: A Volume in the Comparative Religious Ideas Project, edited by Robert Cummings Neville, 43-63. Albany: State University of New York Press.

Dasgupta, S.N. (1973) A History of Indian Philosophy. Vol. I. Cambridge: Cambridge University Press.

The Vaisesika darsana is a system of ontology – it is concerned with ordering and classifying the universe into fundamental components and categories. It is therefore pluralistic and also realistic. The term Vaisesika means “particularist” and is based on the term visesa, meaning “particulars” (Raju 143). Visesa is one of the seven categories into which Vaisesika thinkers organize the universe and figures prominently into its composition. The darsana was founded by Kanada, who authored the Vaisesikasutras circa 400 B.C. (Raju 143).

The doctrine espouses seven categories of reality, called padarthas, which comprise all objects that can be perceived through any means logical or sensory (Hiriyanna 231). They are dravya (substance), guna (quality), karma (motion or activity), samanya (generality or universality), visesa (particularity), samavaya (inherence) and abhava (negation) (Raju 143). Dravya, guna, and karma define the observable physical nature and capabilities of objects, while the existence samanya, visesa and samavaya is demonstrated by logical discrimination. They are also subdivided into further categories.

Dravya can be understood as “that in which qualities inhere” (Raju 143). Dravya is split into two classes of substance, the first of which comprise the nonmaterial world. Firstly there are dis (space), and kala (time), each of which is eternal, infinite and indestructible. There is the mind, manas, which is separate from consciousness and more accurately seen as the integration of the physical senses and the ability to focus on it or selective elements of it (Hiriyanna 231). It is believed to be atomic in scale as the elements are and also the sensory object responsible for emotion and some physical sensations (Raju 148). Finally, there is atman, variously translated as “Self” or “consciousness.” This is consciousness in the overarching sense that is separate and yet observant of the body, senses, mind and other constituent elements of a single person – for each individual, there is a unique atman (Raju 146). The atmans are regarded as infinite and not located in physical space.

The second class comprises the physical world. They are the elements (bhutas): prthivi (earth), apas (water), tejas (light/fire), and vayu (air), which are composed of infinitesimally minute particles called paramanu. Therefore, Vaisesika is also an atomic theory – it proposes the existence of indivisible, imperceptibly tiny component particles of all physical substances. Paramanu are too small to have mass. Accordingly, two combine into a dyad, three of which combine into a triad, which is the minimum observable particle with mass (Raju 145). In addition, each of the four types of paramanu have inherent qualities – prthivi corresponds to smell, apas to taste, tejas to colour and vayu to touch. These are explained as the universal phenomena that allow those senses to function – light, for instance, is seen as necessary to perceive colour. Akasa (aether) is also one of the elements, but is not atomic. It is singular, universal and indivisible like dis and kala. The first four are directly perceivable, but the fifth can only be inferred (Raju 144).

Gunas, or qualities, are traits inherent to dravyas. There are 24 in total: “[C]olor, taste, smell, touch, number, quantity, separateness, contact, disjoining, distance, nearness, knowledge, pleasure, pain, will, aversion and effort… heaviness, liquidity, oiliness, impression, fate [which includes merits as well as demerits, and therefore counts as two], and sound” (Bhattacharyya 143). The most significant are the dual qualities Bhattacharyya lumps together as “fate,” more accurately translated as merit (dharma) and demerit (adharma). These qualities are seen as inherent to substances, but it is possible to conceive of them separate of any object or substance. Colour can be conceived of formlessly, for example. As such, they are considered a distinct category of existence (Hiriyanna 232). Gunas may not have further gunas – there is a distinction made between a quality such as taste and a visesana (variance/mode), such as sweetness. Generally, the distinction is that things considered “qualities” that are attributed to gunas may be scaled – a taste may be sweet or sour, but sweetness and sourness cannot be conceived of without the category of taste – therefore they are subordinate to it (Raju 148).

Karma here refers to action, meaning types of movement. They are rising and falling motion, contraction, expansion and composite or combined motion (e.g. the motions of a human leg) (Raju 149). These are seen as properties of the dravyas as well, although dis, kala and akasa are said to lack motion as they are infinite (Hiriyanna 233).

Samanya translates as “generality” or “universality” and refers to the inherent identifying nature of things. That is, the generic nature of “dogness” that makes all dogs recognizable as such – the combination of dravyas, gunas and karmas unique to dogs (Kak 12). That combination is the same for all dogs – there is one samanya of dogs, which is distinct from the samanya of cows, and so on (Hiriyanna 233).

Visesa, particularity, is the quality that defines two otherwise indistinguishable objects as separate. It is not physically observable itself, but inferred from the fact that two identical things exist in the first place. This is not used lightly – it is only applied to truly indistinguishable objects, which are atomic in scale. While two physical objects can almost always be distinguished from one another by some variance in their gunas, this quality is what distinguishes one atom from the next (Hiriyanna 235). It is also how manases or minds are said to be distinct from one another, as they are also believed to be atomically tiny (Raju 152).

Samavaya proposes the relationships binding these other categories together in coherent manners. It means “inherence” and refers to definitional relationships between inseperable concepts. Substances have this relationship with qualities and with actions, as each (that is, the gunas and karmas) would cease to have value without the former. Likewise, for samanya to be distinct, there must also be visesa, so their relationship is inseparable and necessary (Hiriyanna 236).

The seventh category, abhava, is not an original component of Kanada’s Vaisesikasutras. The category of negation was added as a logical extension of the system. Essentially it addresses the absence of an expected phenomena, object or truth. For example, if an observer is seeking an object and finds that it is missing, the cognized absence of the object is considered a negation – the observer is conceiving of the absence of the object as a distinct phenomenon (Raju 153). Abhava outlines several distinct types of negation – pragabhava and dhvamsabhava refer to the conceptions of an object in the periods before it has been created (e.g. visualizing a home before it has been built) and after it has been destroyed (e.g. remembering a favourite childhood toy, or looking at the broken pieces of an object and recalling its former configuration) to name two (Hiriyanna 238).

The atomic explanation of the composition of the universe begs the question – how is the universe originated? What is the material cause of the paramanu themselves? Later Vaisesika proponents theorize the existence of a God, called Isvara, responsible for creating them – and therefore, the universe. God is conceived of with no identity in particular – it is not Siva, Brahma, etc. Rather, God is the product of logical inference – the universe itself must have a material cause, there appears to be physical order to it suggestive of a controlling “lawmaker,” and the apparent existence of moral order implies an entity dispensing justice (Hiriyanna 243). Kanada himself did not include God in the Vaisesikasutra, but later philosophers such as Sridhara and Udayana consider its existence necessary to explain origination (Hiriyanna 244).

The Nyaya Darsana (or simply Nyaya) is one of the six orthodox Hindu schools of philosophy. It is highlighted as essentially being a school of logical thought, debate and reasoning. The word Nyaya itself may be translated as “right” or “justice” and therefore its practice, Nyaya-Sastra, translates as “the science of right judgement”. The school has a long history, with its first relevant text – the Nyaya-Sutras – purportedly composed by one Aksapada Gautama (or otherwise rendered Gotama) around 150CE (Vidyabhusana 1978:40-41).

Historical Overview:

Nyaya may be regarded as one of several schools of logic (Hindu and otherwise) that have flourished in and around the Indian subcontinent. Prior to the advent of Nyaya as a recognized branch of philosophy it was preceded by the Anviksiki (literally translated as philosophy) dating back as far as 1500BCE. This school bore a close resemblance to Nyaya as it was characterized by a rigorous study of the nature of the soul, and utilized similar technical principles such as tarka (reason), pramana (proof or evidences, and later means of cognition), and prameya (object of knowledge or cognition). So prominent was this system of philosophy that the Mahabharata records the exploits of the legendary Anviksiki practitioner Astavakra. This Anviksiki sage, on one occasion in his youth confounded a renowned sophist named Vandin, in a battle of wits that ended in Vandin’s death. Sometime during the 6th century BCE, the Anvisiki school divided into a school dedicated to pure philosophical speculation and a school dedicated to logic, which likely gave root to the Nyaya Darsana (Vidyabhusana 1978: 1,13-15).

The history and development of Nyaya as a self-contained school began roughly around 1CE. In this first century, the personality of Narada as a foremost expert in Nyaya-sastra becomes apparent as a character in the Mahabharata displaying expert deductive skills whose life intertwined with the likes of Krsna and the god Brahma. Although Narada was a legendary character there is speculation that he was also based on a real life practitioner of Nyaya-sastra (Naiyayika), to whom several aphorisms in Nyaya literature are attributed (Vidyabhusana 1978:40-44).

The formalisation of the school and its system of logic occurred as a result of the work of one Aksapada Gautama, who was the purported author of the Nyaya-Sutras. Significant mystery surrounds Aksapada as much of his persona is equated with far fetched myths involving the unusual title-name Aksapada derived from “aksa” meaning eye and “pada” meaning feet. One such myth details how Gautama, in a state of absent minded philosophical contemplation fell into a well, and upon his rescue was gifted with eyes in his feet to prevent further accidents due to his contemplative tendencies. It has also been speculated that Aksapada and Gautama may have been separate individuals that each contributed to the Nyaya philosophy [For a more detailed discussion of the identity of Gautama see Vidyabhusana (1975:i-xvi)]. Whatever the identity of the original author(s), the Nyaya-Sutras contain several quotations from Buddhist texts and references other Hindu philosophies which date to the 3rd and 4th centuries CE, which demonstrates that the work available today has been altered from its original form by these additions (Vidybhusana 1978: 46-50).

From the 4th century CE till the 13th century CE the practice of Nyaya-sastra became less popular as Buddhist and Jain forms of logic became more prominent and was in addition considered a heterodox philosophy generally (Vidyabhusana 1978: 152, 157). It was however during the 11th and 12th century CE that Nyaya Darsana became recognized as one of the six Saddarsana (orthodox schools or philosophies). This incorporation may have been due to the school actively supporting the authenticity and teachings of the Vedas. In addition this induction coincided with the recognition of the Naiyayikas as saivas or worshippers of Siva. These several factors likely contributed to the Nyaya school being adopted as an orthodox philosophy (Vidyabhusana 1978:152-156).

The latest significant contribution made to the Nyaya philosophy was the so called Navya-Nyaya or “New-Nyaya”. The philosopher Gangesvara Upadhyaya (or simply Gangesa) was purported to have composed the work called the Tattva-Cintamani. Ganesa, similar to the other contributors discussed, was himself mythologized as being gifted with a boon of logical reasoning by the goddess Kali due to a sacrificial offering. The Tattva-Cintamani was in use from the middle of the 15th century among Mithila Brahmans, and became popularized after the establishment of the Navadvipa University in 1503, which allowed its influence to spread throughout India. This text has been largely responsible for the adoption of the Navya-Nyaya variant of logic in pre-modern India (Vidyabhusana 1978:405-406).

The Classical Nyaya Logic System

The Nyaya-Sutras propose sixteen categories (padarthas) which are meant to represent all that can and does exist. These sixteen categories in order of discussion are instrument of cognition (pramana), object of cognition (prameya), doubt (samsaya), the objective (prayojana), familiar instance (drstanta), established tenet (siddhanta), member (avayava), disputation (tarka), ascertainment (nirnaya), discussion (vada), rejoinder (jalpa), cavil (vitanda), fallacy (hetvadhasa), quibble (chala), legitimate objection (jati) and deficiency (nigrahasthana) (Junankar 3). This extensive list has, however, been reduced by subsequent commentators on the Nyaya-Sutras to only include the first two categories, pramana and prameya. This is due to the following fourteen padarthas being included within the definition of pramana or prameya, as pramana pertains to the observer while prameya pertains to that which is observed. Therefore the investigation of pramana and prameya forms the foundation of the classical Nyaya Darsana. It is of note however that the Nyaya-Sutras ascribe equal importance and relevance to each of these sixteen categories (Junankar 11-12).

Pramana:

The concept of pramana as translated roughly means instrument or means of cognition and realization. According to the Nyaya–Sutras the padartha, pramana may be further broken down to four forms of valid observation; perception, inference, verbal testimony and analogy (Junankar 12; Vidyabhusana 1975: 2-4). To these four pramana subcategories (or pramanas) four other methods of pramana are suggested; historical tradition, inclusion, implication and absence. These additional pramanas are however dismissed as being included within the scope of the first four (Junankar 38-44). The pramana of perception (pratyaksa) is considered foremost of the four pramanas. It is defined by the Naiyayikas as a sensory cognition of an object that is not itself flawed. This pramana within the framework of classical Nyaya requires an interface or contact between the self and sensory input. Furthermore, the self or atman must make contact with the mind and the senses with the object in order for perception to take effect. This system substantiates a clearly materialistic nature to the philosophy that places personal witness above other forms of cognition (Junankar 47-51). These are based on the use of the five senses (touch, hearing, sight, sound and taste) to apprehend the object in question. However, it also substantiates the existence of and a difference between self (atman) and mind (manas), the self as a transcendent feature of consciousness beyond the mind which in turn produces cognitions from the sense-object contact (Junankar 55-68).

Inference, the second pramana, can be summarized as the act of re-measuring a perception. This is derived from the Sanskrit word anumana, which is comprised of anu meaning “after” and mana meaning “measuring”(Junankar 117). Analogy (upamana) or comparison comes next in the series and “is the knowledge of a thing through its similarity to another thing previously well known”(quoted from the Nyaya-Sutra,Vidyabhusana 1975:3). Lastly, verbal testimony (from sabda meaning sound) which is defined as “the instructive assertion of a reliable person”(quoted from the Nyaya-Sutra, Vidyabhusana 1975: 4) , which according to the Nyaya-Sutra is someone with authority to communicate with regard to the object in question.

Prameya:

Of the two simplified pardarthas there remains prameya, the object of cognition. The prameyas listed in the Nyaya-Sutras are the soul or self (atman), body (sarira), sense organ(indriya), objects of sense (artha), intellect or apprehension (buddhi), mind (manas), activity (pravrtti), fault or defect (dosa), transmigration (pretyabhava), fruit or result (phala),pain (duhkha), and release (apavarga) (Junankar 4; Vidyabhusana 1975: 5-7). Of these prameyas the self (atman) and release from pain (apavarga), are of special importance. According to the Naiyayikas the self is the first prameya perceived, and the perception of the self leads to the perception and cognition of the other prameyas. Release or apavarga is in fact the ultimate goal of the Nyaya-Darsana, and is characterized by a release of the self from pain and pleasure in the attainment of bliss (ksema) through tattvajnana or true knowledge of the nature of things. It must be noted that apavarga differs rhetorically from that of liberation or moksa, yet both are correlated with renunciation and have the same semantic meaning in this context. This accomplishment may be met, according to Nyaya philosophy by the obtaining of true knowledge of all things or a true knowledge of the padarthas (Junankar 391, 465-467;Vidyabhusana 1975: 1).

Nyaya System of Proof and Debate:

The system of proof in the Nyaya system revolves around the use of five “steps” or “limbs” which each demarcate a stage in reasoning. These may be illustrated in the following often quoted example [The following is modified from Matilal (1999:4)]:

1) There is a fire on the hill.

2) For there is smoke.

3) Wherever there is smoke, there is fire, as in the kitchen.

4) This is such a case (smoke on the hill).

5) Therefore it is so, there is fire on the hill.

The first step presents the conclusion or thesis, the second explicates some piece of evidence, the third gives an example to uphold the second step. The fourth step instantiates that the case under investigation is like the example mentioned in the third step. The fifth step then simply states the conclusion again as valid. This system of proof was designed not to reflect the essential structure of reasoning, but rather to act as a way of convincing others of the thesis presented in step one. These steps reflect the attitude of debate possessed by ancient Naiyayikas and the goals of their argument structure (Matilal 1999: 4-5).

The classical system of Nyaya debate (katha) according to the Nyaya-Sutras is divided into honest or truth seeking debate (vada), debate that should be won by any means necessary (jalpa) and finally a debate meant to irrevocably and harshly defeat an opponent (vitanda). The first katha, may occur between a master and his students where truth is the ultimate goal, the second between equals where victory (vijaya) is the goal. The third is characterized by a wholesale attack or rebuttal of the opponents view without giving time or credence to the opponent in any form, the goal being to merely dispute the opponents view, not substantiate ones’ own. In fact the enactor vijaya may be considered in a case such that the philosopher possesses no true opinion and is only intent on defeating his opponents’ position (Matilal 1986: 83-86).

Navya-Nyaya and Conclusion:

The New Nyaya or Navya-Nyaya, was introduced as an advancement over the older school of Nyaya. Its system differs in key aspects from the original school of Nyaya, one prominent aspect being the array of padarthas.

The Navya-Nyaya system details only seven padarthas, as opposed to the sixteen detailed by Gautama in the Nyaya-Sutras (though later scholars reduced them to two, as previously discussed). These padarthas are, substance (dravya), quality (guna), action (kriya), generic character or genus (jati), ultimate difference or that which distinguishes one indivisible object from another (visesa), inherence or self relation (samavaya) and absence (abhava). While it is obvious that these categories differ from the padarthas of Gautama, the most significant difference is the last padartha, abhava or the lack of substance (bhava). The recognition of absence as a part of the system allows the Navy-Nyaya logician to attribute the absence of a quality to an object rather than simply not mention it when categorizing objects (Ingalls 37-38). While the theme of absence was explored in the older Nyaya school particularly in application to the apprehension of the absence of an object it was formally dismissed (Junankar 39).

Another interesting feature of the school is the idea employed by its practitioners that all things that exist are knowable, but not necessarily knowable to human minds. They affirm that if it (whatever “it” may be) is not knowable to human minds, it is at least knowable to a god. Hence there is both determinate and indeterminate knowledge. Determinate knowledge is described as that knowledge that allows for a specific object to be distinguished from other objects, which knowledge is usually expressible in language. Indeterminate knowledge on the other hand is held by Naiyayikas to be knowledge which cannot be expressed in linguistic terms as linguistic terms only refer to determinate objects, not indeterminate objects. They therefore affirm that one may only infer the existence of indeterminate knowledge (Ingalls 39).

While the Nyaya Darsana has played a significant role in the development of the religious landscape of India and surrounding areas, in modern times it is largely framed as a subject of the past. Still its impact remains relevant as a realist philosophical contributor to the shape of the philosophical schools of India (Matilal 1986: 1-15).